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This paper explores the application of deep Q-learning to hedging at-the-money options on the S\&P~500 index. We develop an agent based on the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm, trained to simulate hedging…

Computational Finance · Quantitative Finance 2025-10-13 Zofia Bracha , Paweł Sakowski , Jakub Michańków

In finance, sequential decision problems are often faced, for which reinforcement learning (RL) emerges as a promising tool for optimisation without the need of analytical tractability. However, the objective of classical RL is the expected…

Computational Finance · Quantitative Finance 2026-02-13 Federico Cacciamani , Roberto Daluiso , Marco Pinciroli , Michele Trapletti , Edoardo Vittori

We approach the continuous-time mean-variance (MV) portfolio selection with reinforcement learning (RL). The problem is to achieve the best tradeoff between exploration and exploitation, and is formulated as an entropy-regularized, relaxed…

Portfolio Management · Quantitative Finance 2019-05-07 Haoran Wang , Xun Yu Zhou

We propose to solve large scale Markowitz mean-variance (MV) portfolio allocation problem using reinforcement learning (RL). By adopting the recently developed continuous-time exploratory control framework, we formulate the exploratory MV…

Portfolio Management · Quantitative Finance 2019-08-05 Haoran Wang

With the fast development of quantitative portfolio optimization in financial engineering, lots of AI-based algorithmic trading strategies have demonstrated promising results, among which reinforcement learning begins to manifest…

Mathematical Finance · Quantitative Finance 2023-03-10 Huifang Huang , Ting Gao , Pengbo Li , Jin Guo , Peng Zhang , Nan Du

This paper investigates the deep hedging framework, based on reinforcement learning (RL), for the dynamic hedging of swaptions, contrasting its performance with traditional sensitivity-based rho-hedging. We design agents under three…

Risk Management · Quantitative Finance 2025-12-09 Zaniar Ahmadi , Frédéric Godin

Reinforcement learning (RL) is gaining attention by more and more researchers in quantitative finance as the agent-environment interaction framework is aligned with decision making process in many business problems. Most of the current…

Mathematical Finance · Quantitative Finance 2022-05-31 Huifang Huang , Ting Gao , Yi Gui , Jin Guo , Peng Zhang

In financial applications, reinforcement learning (RL) agents are commonly trained on historical data, where their actions do not influence prices. However, during deployment, these agents trade in live markets where their own transactions…

Machine Learning · Computer Science 2026-01-27 Shaocong Ma , Heng Huang

Portfolio management remains a crucial challenge in finance, with traditional methods often falling short in complex and volatile market environments. While deep reinforcement approaches have shown promise, they still face limitations in…

Machine Learning · Computer Science 2025-03-07 Fengchen Gu , Zhengyong Jiang , Ángel F. García-Fernández , Angelos Stefanidis , Jionglong Su , Huakang Li

Reinforcement learning (RL) is a powerful machine learning technique that enables an intelligent agent to learn an optimal policy that maximizes the cumulative rewards in sequential decision making. Most of methods in the existing…

Machine Learning · Statistics 2023-01-06 Chengchun Shi , Zhengling Qi , Jianing Wang , Fan Zhou

We propose a reinforcement learning (RL) framework under a broad class of risk objectives, characterized by convex scoring functions. This class covers many common risk measures, such as variance, Expected Shortfall, entropic Value-at-Risk,…

Mathematical Finance · Quantitative Finance 2025-05-16 Shanyu Han , Yang Liu , Xiang Yu

Reinforcement learning (RL) has shown significant promise for sequential portfolio optimization tasks, such as stock trading, where the objective is to maximize cumulative returns while minimizing risks using historical data. However,…

Machine Learning · Computer Science 2025-05-20 Haochen Yuan , Minting Pan , Yunbo Wang , Siyu Gao , Philip S. Yu , Xiaokang Yang

Abstract In this work, we build two environments, namely the modified QLBS and RLOP models, from a mathematics perspective which enables RL methods in option pricing through replicating by portfolio. We implement the environment…

Pricing of Securities · Quantitative Finance 2022-05-12 Ziheng Chen

We proposed a new Portfolio Management method termed as Robust Log-Optimal Strategy (RLOS), which ameliorates the General Log-Optimal Strategy (GLOS) by approximating the traditional objective function with quadratic Taylor expansion. It…

Portfolio Management · Quantitative Finance 2018-05-02 Yifeng Guo , Xingyu Fu , Yuyan Shi , Mingwen Liu

The inherent volatility and dynamic fluctuations within the financial stock market underscore the necessity for investors to employ a comprehensive and reliable approach that integrates risk management strategies, market trends, and the…

Trading and Market Microstructure · Quantitative Finance 2024-11-13 Alhassan S. Yasin , Prabdeep S. Gill

Portfolio management is the art and science in fiance that concerns continuous reallocation of funds and assets across financial instruments to meet the desired returns to risk profile. Deep reinforcement learning (RL) has gained increasing…

Portfolio Management · Quantitative Finance 2023-10-30 Yinheng Li , Junhao Wang , Yijie Cao

Reinforcement learning (RL) based investment strategies have been widely adopted in portfolio management (PM) in recent years. Nevertheless, most RL-based approaches may often emphasize on pursuing returns while ignoring the risks of the…

Portfolio Management · Quantitative Finance 2023-06-13 Zhenglong Li , Hejun Huang , Vincent Tam

This paper presents a deep reinforcement learning (DRL) framework for dynamic portfolio optimization under market uncertainty and risk. The proposed model integrates a Sharpe ratio-based reward function with direct risk control mechanisms,…

Portfolio Management · Quantitative Finance 2025-11-17 Emmanuel Lwele , Sabuni Emmanuel , Sitali Gabriel Sitali

This paper explores the mean-variance portfolio selection problem in a multi-period financial market characterized by regime-switching dynamics and uncontrollable liabilities. To address the uncertainty in the decision-making process within…

Optimization and Control · Mathematics 2025-09-04 Zhongqin Gao , Ping Chen , Xun Li , Yan Lv , Wenhao Zhang

Black-Scholes (BS) is the standard mathematical model for option pricing in financial markets. Option prices are calculated using an analytical formula whose main inputs are strike (at which price to exercise) and volatility. The BS…

Mathematical Finance · Quantitative Finance 2020-07-14 Tushar Vaidya , Carlos Murguia , Georgios Piliouras